Question

Which statements are true about the ordered pair (7, 19) and the system of equations? {2x−y=−5x+3y=22 Select each correct answer. The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true. The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true. The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false. The ordered pair (7, 19) is a solution to the system because it makes both equations true.

Answer 1

After plugging in the numbers to the equations, I can confirm it's a solution to both. So the correct answers would be the first, the second, and the fourth answers. Because (7, 19) does make the first equation true:

2 * 7 = 14
14 - 19 = -5

And (7, 19) also makes the second equation true:

-5 * 7 = -35
3 * 19 = 57
57 + -35 = 22

Then (7, 9) is a solution for both. Therefore, the first, second, and fourth answers are all true :)

Answer 2

(7,19) is a solution for only the first equation (2x-y= -5), so it is not a solution to the system.
2x-y=-5 we substitute the x and y for 7, and 19 making the equation 2 x 7-19, 2 x 7 is 14 so we then put the 14 and 19 together, 14-19, and 14-19 is equal to -5 so the first equation is true. For the second equation which is x+3y=22 we do the same thing as the first equation, we substitute x and y for 7, and 19, substituting these numbers in we get 7+3 x 19, 3 x 19 is 57, so 7+57, which equals 64 and is no where near 22. So, the ordered pair (7,19) is a solution to the first equation because, it makes the first equation true, and the ordered pair (7,19) is not a solution to the system because, it makes at least one of the equations false.